Who hasn’t, at some point, thought they simply weren’t “good at maths”? Or believed that mathematics was little more than memorising formulas and repeating exercises without really understanding why? This is probably one of the most widespread misconceptions about the subject.
Yet mathematics does not begin with formulas. It grows out of the need to compare, build, recognise patterns, establish relationships, and solve problems. Long before symbols and algorithms come into play, there is the need to manipulate and explore objects, to experience situations that give meaning to mathematical ideas. And much of that exploration begins with our hands, because before we can write mathematics, we need to experience it.
Even today, mathematics is often taught as if it were a finished language that simply needs to be memorised. But decades of research in mathematics education have shown that genuine understanding requires much more: exploring, experimenting, making mistakes, discussing ideas, and trying again. Mathematics is not passively received; it is actively constructed.
This is why manipulatives play such an important role in mathematics education. They are not merely resources for young children or tools to make lessons more engaging. They are thinking tools. They help transform abstract concepts into experiences that can be seen, touched, and understood.
Take Cuisenaire rods, for example. At first glance, they may seem like nothing more than coloured wooden blocks. Yet when they are compared, combined, and arranged, they begin to reveal numerical relationships, equivalences, and different ways of representing the same quantity. Numbers cease to be mere written symbols and become ideas that can be observed and understood. Similarly, a geoboard—a board of evenly spaced pegs used with elastic bands—turns geometric concepts into an experience of discovery. Shapes are no longer simply drawn; they are built, transformed, and explored.
There is, however, one fundamental idea we should never forget: manipulatives do not contain mathematics. They explain nothing on their own. Mathematics emerges through the questions we ask, the relationships we discover, and the reasoning we develop from our experiences. The essential point is not simply to handle objects; it is to think and reason while using them.
This way of understanding learning also has a social dimension. If we want more people to feel capable of understanding mathematics, simplifying the language is not enough. We need to create opportunities for people to experience mathematics, make it visible, and connect it with the world around them. Scientific literacy should not be a privilege reserved for a few; it should be an open door for everyone.
Perhaps the real problem is not that mathematics is difficult. More often than not, the problem lies in the way we present and teach it.
Lecturer in the Department of Mathematics Education at the Faculty of Education Sciences, University of A Coruña. Her work explores how people learn mathematics through hands-on experience, manipulation of materials, and problem-solving. Alongside her teaching and research, she promotes science outreach programs and cultural initiatives aimed at bringing scientific knowledge closer to society.